Finite Group Databasebeta

← #7094857

Subgroups — #7094857

Order 512.

1386 conjugacy classes of subgroups.

The subgroup lattice has 1213 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44951C211yesmaximal, characteristic
2#42850C211yesmaximal, characteristic, complemented
3#32377C211yesmaximal, characteristic, complemented
4#32361C211yesmaximal, characteristic, complemented
5#31636C211yesmaximal, characteristic, complemented
6#31600C211yesmaximal, characteristic, complemented
7#31526C211yesmaximal, characteristic, complemented
8#30964C211yesmaximal, characteristic, complemented
9#30894C211yesmaximal, characteristic, complemented
10#30836C211yesmaximal, characteristic, complemented
11#29531C211yesmaximal, characteristic, complemented
12#29504C211yesmaximal, characteristic
13#28967C211yesmaximal, characteristic, complemented
14#28545C211yesmaximal, characteristic, complemented
15#28433C211yesmaximal, characteristic, complemented
16#27081C211yesmaximal, characteristic
17#26919C211yesmaximal, characteristic, complemented
18#26913C211yesmaximal, characteristic
19#26845C211yesmaximal, characteristic, complemented
20#26829C211yesmaximal, characteristic, complemented
21#26603C211yesmaximal, characteristic
22#26586C211yesmaximal, characteristic
23#26486C211yesmaximal, characteristic, complemented
24#26386C211yesmaximal, characteristic, complemented
25#26379C211yesmaximal, characteristic, complemented
26#26166C211yesmaximal, characteristic, complemented
27#23811C211yesmaximal, characteristic
28#23268C211yesmaximal, characteristic, complemented
29#23012C211yesmaximal, characteristic, complemented
30#22671C211yesmaximal, characteristic, complemented
31#22231C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#491C2211yescharacteristic
34C2×#491C2211yescharacteristic
35C2×#479C2211yescharacteristic
36C2×#477C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#461C2211yescharacteristic
39C2×#461C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×#440C2211yescharacteristic
43C2×#440C2211yescharacteristic
44C2×C4×SD16C2211yescharacteristic
45C2×C4×SD16C2211yescharacteristic
46C2×C4×SD16C2211yescharacteristic
47#2839—21no—
48#2810—21no—
49#2802—21no—
50#2794—21no—
51#2791—21no—
52#2780—21no—
53#2780—21no—
54#2748—21no—
55#2732—21no—
56#2655—21no—
57#2655—21no—
58#2645C2211yescharacteristic
59#2590—21no—
60#2570C2211yescharacteristic
61#2566C2211yescharacteristic
62#2565C2211yescharacteristic
63#2564—21no—
64#2550C2211yescharacteristic
65#2546C2211yescharacteristic
66#2542C2211yescharacteristic
67#2511C2211yescharacteristic
68#2509C2211yescharacteristic
69#2487—21no—
70#2454C2211yescharacteristic
71#2454C2211yescharacteristic
72#2454C2211yescharacteristic
73#2453C2211yescharacteristic
74#2453C2211yescharacteristic
75#2452C2211yescharacteristic
76#2450—21no—
77#2449—21no—
78#2446C2211yescharacteristic
79#2446C2211yescharacteristic
80#2446C2211yescharacteristic
81#2446C2211yescharacteristic
82#2402C2211yescharacteristic
83#2366C2211yescharacteristic
84#2366C2211yescharacteristic
85#2365C2211yescharacteristic
86Q8×C4⋊C4C2211yescharacteristic
87#2349C2211yescharacteristic
88D4×C4⋊C4C2211yescharacteristic
89#2330C2211yescharacteristic
90#2328C2211yescharacteristic
91#2327C2211yescharacteristic
92#2099C2211yescharacteristic
93#2097C2211yescharacteristic
94#2097C2211yescharacteristic
95#2097C2211yescharacteristic
96#2096C2211yescharacteristic
97#2095C2211yescharacteristic
98#2093C2211yescharacteristic
99#2092C2211yescharacteristic
100#2092C2211yescharacteristic
101#2088C2211yescharacteristic
102#2085C2211yescharacteristic
103#2085C2211yescharacteristic
104#2084C2211yescharacteristic
105#2074C2211yescharacteristic
106#2072C2211yescharacteristic
107#2068C2211yescharacteristic
108#2068C2211yescharacteristic
109#2067C2211yescharacteristic
110#2066C2211yescharacteristic
111#2065C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2059C2211yescharacteristic
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic
118#2043C2211yescharacteristic
119#2043C2211yescharacteristic
120#2041C2211yescharacteristic
121#2026C2211yescharacteristic
122#2025C2211yescharacteristic
123#2024C2211yescharacteristic
124#2024C2211yescharacteristic
125#2014C2211yescharacteristic
126#2014C2211yescharacteristic
127#2014C2211yescharacteristic
128#2013C2211yescharacteristic
129#2013C2211yescharacteristic
130#2013C2211yescharacteristic
131#2013C2211yescharacteristic
132#1991C2211yescharacteristic
133#1973C2211yescharacteristic
134#1973C2211yescharacteristic
135#1973C2211yescharacteristic
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1960C2211yescharacteristic
139#1956C2211yescharacteristic
140#1949C2211yescharacteristic
141#1944C2211yescharacteristic
142#1944C2211yescharacteristic
143#1944C2211yescharacteristic
144#1942C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1935C2211yescharacteristic
148#1935C2211yescharacteristic
149#1934C2211yescharacteristic
150#1933C2211yescharacteristic
151#1933C2211yescharacteristic
152#1928C2211yescharacteristic
153#1928C2211yescharacteristic
154#1928C2211yescharacteristic
155#1927C2211yescharacteristic
156#1927C2211yescharacteristic
157#1927C2211yescharacteristic
158#1925C2211yescharacteristic
159#1921C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1917C2211yescharacteristic
163#1917C2211yescharacteristic
164#1917C2211yescharacteristic
165#1917C2211yescharacteristic
166#1917C2211yescharacteristic
167#1916C2211yescharacteristic
168#1916C2211yescharacteristic
169#1916C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1865C2211yescharacteristic
183#1864C2211yescharacteristic
184#1864C2211yescharacteristic
185#1864C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1863C2211yescharacteristic
189#1863C2211yescharacteristic
190#1862C2211yescharacteristic
191#1862C2211yescharacteristic
192#1847C2211yescharacteristic
193#1845C2211yescharacteristic
194#1803C2211yescharacteristic
195#1802C2211yescharacteristic
196#1771C2211yescharacteristic
197#1771C2211yescharacteristic
198#1771C2211yescharacteristic
199#1770C2211yescharacteristic
200#1762C2211yescharacteristic
201#1746C2211yescharacteristic
202#1746C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×D4—21no—
226C2×C4×D4—21no—
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C22×C4⋊C4—21no—
234#501—42no—
235#491—24no—
236#491—42no—
237#479—42no—
238#478—42no—
239#477—42no—
240#461—24no—
241#461—42no—
242#440—42no—
243#440—42no—
244#440—42no—
245#440—42no—
246C4×SD16—24no—
247C4×SD16—42no—
248C4×SD16—42no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#401—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400D411yescharacteristic
319#400D411yescharacteristic
320#400D411yescharacteristic
321#400D411yescharacteristic
322#399—21no—
323#399—21no—
324#399—21no—
325#399—21no—
326#399—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398D411yescharacteristic
340#398D411yescharacteristic
341#398D411yescharacteristic
342#398D411yescharacteristic
343#396—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#395—21no—
350#393—21no—
351#391—21no—
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#390—21no—
363#390—21no—
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389—21no—
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#384—21no—
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#382C2311yescharacteristic
441#382C2311yescharacteristic
442#382C2311yescharacteristic
443#380—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459#376C2311yescharacteristic
460C2×#95—21no—
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C22×Q8—21no—
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C2411yescharacteristic
500C22×D4C2411yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—41no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C4⋊Q8—22no—
534C4⋊Q8—22no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541#127—22no—
542#127—22no—
543#125—22no—
544#125—41no—
545#125—41no—
546#125—41no—
547#125—41no—
548#125—41no—
549C22⋊Q8—82no—
550C22⋊Q8—82no—
551C22⋊Q8—82no—
552C4×Q8—22no—
553C4×Q8—41no—
554C4×Q8—41no—
555C4×Q8—41no—
556C4×Q8—41no—
557C4×Q8—41no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—82no—
575C4×D4—82no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—82no—
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669#107—22no—
670#107—22no—
671#107—22no—
672#107—41no—
673#107—41no—
674#107—41no—
675#107—41no—
676#107—41no—
677#106—22no—
678#106—22no—
679#106—41no—
680#106—41no—
681#106—41no—
682#106—41no—
683C4⋊C8—22no—
684C4⋊C8—22no—
685C4⋊C8—22no—
686C4⋊C8—41no—
687#103—22no—
688#103—22no—
689#103—22no—
690#103—22no—
691#103—22no—
692#103—22no—
693#103—22no—
694#103—22no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#103—41no—
703#103—41no—
704#103#4114yes—
705#102—22no—
706#102—22no—
707#102—22no—
708#102—22no—
709#102—22no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#97—22no—
716#97—22no—
717#97—22no—
718#97—22no—
719#97—41no—
720C4×C8—22no—
721C4×C8—22no—
722C4×C8—41no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780C24—21no—
781C24—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—42no—
800C2×Q8—81no—
801C2×Q8—81no—
802C2×Q8C2×#4112yes—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—81no—
816C2×D4—81no—
817C2×D4—81no—
818C2×D4—81no—
819C2×D42−1+412yes—
820C2×D42−1+412yes—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C2511yescharacteristic
868SD16—28no—
869SD16—44no—
870SD16—44no—
871SD16—44no—
872SD16—44no—
873SD16—82no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8C2×#4112yes—
896C2×C8H(5,𝔽2)12yes—
897C2×C8H(5,𝔽2)12yes—
898C4⋊C4—22no—
899C4⋊C4—22no—
900C4⋊C4—22no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—41no—
923C4⋊C4—41no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—41no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4C2×#4112yes—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—42no—
1001C42—81no—
1002C42—81no—
1003C42—81no—
1004C42—81no—
1005C42—81no—
1006C42—81no—
1007C42—81no—
1008C23—22no—
1009C23—22no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23C23×D411yescharacteristic
1023Q8—22no—
1024Q8—22no—
1025Q8—41no—
1026Q8—41no—
1027Q8—41no—
1028Q8—41no—
1029Q8—41no—
1030Q8—41no—
1031Q8—41no—
1032Q8—41no—
1033Q8—41no—
1034Q8—41no—
1035Q8—162no—
1036D4—22no—
1037D4—22no—
1038D4—22no—
1039D4—22no—
1040D4—41no—
1041D4—41no—
1042D4—41no—
1043D4—41no—
1044D4—84no—
1045D4—84no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—84no—
1130C2×C4—162no—
1131C2×C4—162no—
1132C2×C4—162no—
1133C2×C4—162no—
1134C2×C4—162no—
1135C2×C4#57712yes—
1136C2×C4C22×#4111yescharacteristic
1137C2×C4C2×H(5,𝔽2)11yescharacteristic
1138C2×C4C2×H(5,𝔽2)11yescharacteristic
1139C2×C4C2×2−1+411yescharacteristic
1140C2×C4C2×2−1+411yescharacteristic
1141C2×C4#58511yescharacteristic
1142C8—22no—
1143C8—22no—
1144C8—22no—
1145C8—41no—
1146C8—41no—
1147C8—41no—
1148C8—41no—
1149C8—41no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—42no—
1156C22—81no—
1157C22—81no—
1158C22—81no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22D4×#4111yescharacteristic
1165C22#348611yescharacteristic
1166C22#349811yescharacteristic
1167C22C2×#57711yescharacteristic
1168C22#358511yescharacteristic
1169C22#358611yescharacteristic
1170C22#358611yescharacteristic
1171C4—22no—
1172C4—41no—
1173C4—41no—
1174C4—41no—
1175C4—42no—
1176C4—41no—
1177C4—41no—
1178C4—41no—
1179C4—41no—
1180C4—41no—
1181C4—42no—
1182C4—41no—
1183C4—41no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—81no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4#349211yescharacteristic
1200C4#352011yescharacteristic
1201C4#353511yescharacteristic
1202C4#354111yescharacteristic
1203C2—82no—
1204C2—82no—
1205C2#4429211yescharacteristic
1206C2#6151511yescharacteristic
1207C2#6152011yescharacteristic
1208C2#6184811yescharacteristic
1209C2#6187311yescharacteristic
1210C2#6244211yescharacteristic
1211C2#6246511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#127C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2402 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #42850C2semidirect
3. #32377C2semidirect
4. #32361C2semidirect
5. #31636C2semidirect
6. #31600C2semidirect
7. #31526C2semidirect
8. #30964C2semidirect
9. #30894C2semidirect
10. #30836C2semidirect
11. #29531C2semidirect
13. #28967C2semidirect
14. #28545C2semidirect
15. #28433C2semidirect
17. #26919C2semidirect
19. #26845C2semidirect
20. #26829C2semidirect
23. #26486C2semidirect
24. #26386C2semidirect
25. #26379C2semidirect
26. #26166C2semidirect
28. #23268C2semidirect
29. #23012C2semidirect
30. #22671C2semidirect
31. #22231C2semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#449512
#428502
#323772
#323612
#316362
#316002
#315262
#309642
#308942
#308362
#295312
#295042
#289672
#285452
#284332
#270812
#269192
#269132
#268452
#268292
#266032
#265862
#264862
#263862
#263792
#261662
#238112
#232682
#230122
#226712
#222312